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Application-level multicast (ALM) communications replicate packets on host level to deliver them from a single source to multiple clients, so that it can efficiently realize a variety of network applications using moving pictures such as video conferences, distance learning, and video-on-demands. In this paper, we propose the CT+ (compact tree plus) algorithm for finding a better ALM routing tree in terms of delay minimization between hosts. CT+ consists of a tree construction stage from the existing CT algorithm, and a newly added iterative tree improvement stage. Then, we define the extended ALM routing problem and its heuristic algorithm ExCT+, to optimize the effectiveness of the multihome network in ALM communications by selecting multihomed hosts and connections in the ALM routing tree simultaneously. For their evaluations, we construct a network simulation model named MINET (multiple-ISP network simulator), where the topology is composed of multiple ISP backbone networks with IX connections, and the network traffic is generated by following the M/M/1 queuing process. The simulation results using MINET verify the effectiveness of our algorithms.